In this talk, we first, classify the numerical methods for partial differential equations including the domain methods, the boundary element method and the meshfree methods. Based on the advantages of meshfree methods, we then focus on these methods and their classifications. The meshfree methods is classified bases on the kinds of formulation, the choice of approximate functions and the sort of domain representation. Regarding the formulation, we compare the strong forms, weak forms and weak-strong forms formulation and highlight the advantages of each method. The choice of approximate functions, can be carried out based on interpolation, lease square and moving least square methods. We proceed with considering the recent developments of local and global weak-form meshless methods.
